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A question in Time Series:

We have Augmented Dickey-Fuller (ADF) test to test the stationarity of time series. But it seems that this test behaves weirdly. Even for time series which obviously look non-stationary just by looking at it, this test says that it is stationary. For example, check the result of this test for the "AirPassengers" dataset, it will give you a p-value of less than 0.01 (< 0.05), which suggests that the series is stationary. This seems to be misleading.

Some resources say that this test checks if the characteristic equation of the series has a unit root. Stationary series have roots > 1.

Can someone help me with this? What is correct here?

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    $\begingroup$ Indeed, the augmented Dickey-Fuller test is a test for presence of unit root in a time series. This is the only form of nonstationarity it tests for. $\endgroup$ – Richard Hardy Apr 25 '18 at 6:10

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